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Cost of Inflation in Inventory Theoretical Models

Author

Listed:
  • Fernando Alvarez

    (University of Chicago)

  • Francesco Lippi

    (Istituto Einaudi)

  • Roberto Robatto

    (University of Wisconsin)

Abstract

We show that the area under the long-run demand curve for money approximates the welfare cost of inflation for a large class of inventory theoretical models of money demand. The class of inventory models considered has a general stochastic structure of the net cash expenditures, as well as of the fixed/variable cost of withdrawing and depositing money. Thus, our framework nests a large number of models that have been studied in the literature. The results complement those obtained by Lucas (2000) for money-in-the-utility function and for shopping-time models. (Copyright: Elsevier)

Suggested Citation

  • Fernando Alvarez & Francesco Lippi & Roberto Robatto, 2019. "Cost of Inflation in Inventory Theoretical Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 32, pages 206-226, April.
  • Handle: RePEc:red:issued:18-233
    DOI: 10.1016/j.red.2018.11.001
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    1. J. Michael Harrison & Michael I. Taksar, 1983. "Instantaneous Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 439-453, August.
    2. John Bagnall & David Bounie & Kim P. Huynh & Anneke Kosse & Tobias Schmidt & Scott Schuh, 2016. "Consumer Cash Usage: A Cross-Country Comparison with Payment Diary Survey Data," International Journal of Central Banking, International Journal of Central Banking, vol. 12(4), pages 1-61, December.
    3. Orazio P. Attanasio & Luigi Guiso & Tullio Jappelli, 2002. "The Demand for Money, Financial Innovation, and the Welfare Cost of Inflation: An Analysis with Household Data," Journal of Political Economy, University of Chicago Press, vol. 110(2), pages 317-351, April.
    4. Patrick Bolton & Hui Chen & Neng Wang, 2011. "A Unified Theory of Tobin's q, Corporate Investment, Financing, and Risk Management," Journal of Finance, American Finance Association, vol. 66(5), pages 1545-1578, October.
    5. Leigh A. Riddick & Toni M. Whited, 2009. "The Corporate Propensity to Save," Journal of Finance, American Finance Association, vol. 64(4), pages 1729-1766, August.
    6. Robert E. Lucas, 2001. "Inflation and Welfare," International Economic Association Series, in: Axel Leijonhufvud (ed.), Monetary Theory as a Basis for Monetary Policy, chapter 4, pages 96-142, Palgrave Macmillan.
    7. Ricardo Lagos & Randall Wright, 2005. "A Unified Framework for Monetary Theory and Policy Analysis," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 463-484, June.
    8. Bar-Ilan, Avner & Perry, David & Stadje, Wolfgang, 2004. "A generalized impulse control model of cash management," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1013-1033, March.
    9. J. Michael Harrison & Thomas M. Sellke & Allison J. Taylor, 1983. "Impulse Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 454-466, August.
    10. Alvarez, Fernando & Lippi, Francesco, 2013. "The demand of liquid assets with uncertain lumpy expenditures," Journal of Monetary Economics, Elsevier, vol. 60(7), pages 753-770.
    11. Boris Nikolov & Toni M. Whited, 2014. "Agency Conflicts and Cash: Estimates from a Dynamic Model," Journal of Finance, American Finance Association, vol. 69(5), pages 1883-1921, October.
    12. William J. Baumol, 1952. "The Transactions Demand for Cash: An Inventory Theoretic Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 66(4), pages 545-556.
    13. Carlos E. da Costa & Iván Werning, 2008. "On the Optimality of the Friedman Rule with Heterogeneous Agents and Nonlinear Income Taxation," Journal of Political Economy, University of Chicago Press, vol. 116(1), pages 82-112, February.
    14. Luigi Guiso & Chaoqun Lai & Makoto Nirei, 2017. "An Empirical Study of Interaction-Based Aggregate Investment Fluctuations," The Japanese Economic Review, Japanese Economic Association, vol. 68(2), pages 137-157, June.
    15. Raj Chetty, 2009. "Sufficient Statistics for Welfare Analysis: A Bridge Between Structural and Reduced-Form Methods," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 451-488, May.
    16. Fernando Alvarez & Francesco Lippi, 2009. "Financial Innovation and the Transactions Demand for Cash," Econometrica, Econometric Society, vol. 77(2), pages 363-402, March.
    17. Scott R. Baker & Stephanie Johnson & Lorenz Kueng, 2021. "Shopping for Lower Sales Tax Rates," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(3), pages 209-250, July.
    18. Jovanovic, Boyan, 1982. "Inflation and Welfare in the Steady State," Journal of Political Economy, University of Chicago Press, vol. 90(3), pages 561-577, June.
    19. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    20. Alvarez, Fernando & Lippi, Francesco, 2017. "Cash burns: An inventory model with a cash-credit choice," Journal of Monetary Economics, Elsevier, vol. 90(C), pages 99-112.
    21. Fernando Alvarez & Hervé Le Bihan & Francesco Lippi, 2016. "The Real Effects of Monetary Shocks in Sticky Price Models: A Sufficient Statistic Approach," American Economic Review, American Economic Association, vol. 106(10), pages 2817-2851, October.
    22. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    23. Luigi Guiso & Giuseppe Parigi, 1999. "Investment and Demand Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(1), pages 185-227.
    24. He, Ping & Huang, Lixin & Wright, Randall, 2008. "Money, banking, and monetary policy," Journal of Monetary Economics, Elsevier, vol. 55(6), pages 1013-1024, September.
    25. Lucas, Robert E, Jr & Stokey, Nancy L, 1987. "Money and Interest in a Cash-in-Advance Economy," Econometrica, Econometric Society, vol. 55(3), pages 491-513, May.
    26. Jacob A. Frenkel & Boyan Jovanovic, 1980. "On Transactions and Precautionary Demand for Money," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(1), pages 25-43.
    27. Costas Arkolakis & Arnaud Costinot & Andres Rodriguez-Clare, 2012. "New Trade Models, Same Old Gains?," American Economic Review, American Economic Association, vol. 102(1), pages 94-130, February.
    28. Sanches, Daniel & Williamson, Stephen, 2010. "Money and credit with limited commitment and theft," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1525-1549, July.
    29. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
    30. Bar-Ilan, Avner, 1990. "Trigger-Target Rules Need Not Be Optimal with Fixed Adjustment Costs: A Simple Comment on Optimal Money Holding under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 229-234, February.
    31. André C. Silva, 2012. "Rebalancing Frequency and the Welfare Cost of Inflation," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(2), pages 153-183, April.
    32. Merton H. Miller & Daniel Orr, 1966. "A Model of the Demand for Money by Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(3), pages 413-435.
    33. Markus K. Brunnermeier & Yuliy Sannikov, 2014. "A Macroeconomic Model with a Financial Sector," American Economic Review, American Economic Association, vol. 104(2), pages 379-421, February.
    34. John Bagnall & David Bounie & Kim P. Huynh & Anneke Kosse & Tobias Schmidt & Scott Schuh, 2016. "Consumer Cash Usage: A Cross-Country Comparison with Payment Diary Survey Data," International Journal of Central Banking, International Journal of Central Banking, vol. 12(4), pages 1-61, December.
    35. Luca Benati, 2018. "Long-Run Money Demand Redux," Diskussionsschriften dp1804, Universitaet Bern, Departement Volkswirtschaft.
    36. Bar-Ilan, Avner, 1990. "Overdrafts and the Demand for Money," American Economic Review, American Economic Association, vol. 80(5), pages 1201-1216, December.
    37. Blyth C. Archibald & Edward A. Silver, 1978. "(s, S) Policies Under Continuous Review and Discrete Compound Poisson Demand," Management Science, INFORMS, vol. 24(9), pages 899-909, May.
    38. Milbourne, Ross, 1983. "Optimal Money Holding under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 685-698, October.
    39. Kenneth Rogoff, 1998. "Blessing or curse? Foreign and underground demand for euro notes," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 13(26), pages 262-303.
    40. Ricardo Lagos & Guillaume Rocheteau & Randall Wright, 2017. "Liquidity: A New Monetarist Perspective," Journal of Economic Literature, American Economic Association, vol. 55(2), pages 371-440, June.
    41. George M. Constantinides & Scott F. Richard, 1978. "Existence of Optimal Simple Policies for Discounted-Cost Inventory and Cash Management in Continuous Time," Operations Research, INFORMS, vol. 26(4), pages 620-636, August.
    42. Martin Weitzman, 1968. "A Model of the Demand for Money by Firms: Comment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(1), pages 161-164.
    43. Lucas, Robert E. & Nicolini, Juan Pablo, 2015. "On the stability of money demand," Journal of Monetary Economics, Elsevier, vol. 73(C), pages 48-65.
    44. Agnès Sulem, 1986. "A Solvable One-Dimensional Model of a Diffusion Inventory System," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 125-133, February.
    45. Eppen, Gary D & Fama, Eugene F, 1969. "Cash Balance and Simple Dynamic Portfolio Problems with Proportional Costs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(2), pages 119-133, June.
    46. Merton H. Miller & Daniel Orr, 1968. "The Demand For Money By Firms: Extensions Of Analytic Results," Journal of Finance, American Finance Association, vol. 23(5), pages 735-759, December.
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    2. Bernardino Adão & André C. Silva, 2021. "Government financing, inflation, and the financial sector," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1357-1396, June.
    3. Martin Brown & Nicole Hentschel & Hannes Mettler & Helmut Stix, 2020. "Financial Innovation, Payment Choice and Cash Demand - Causal Evidence from the Staggered Introduction of Contactless Debit Cards," Working Papers on Finance 2002, University of St. Gallen, School of Finance.
    4. Luca Benati & Juan-Pablo Nicolini, 2019. "The Welfare Costs of Inflation," Diskussionsschriften dp1911, Universitaet Bern, Departement Volkswirtschaft.

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    More about this item

    Keywords

    Money demand; Welfare cost of inflation; Inventory theoretical models;
    All these keywords.

    JEL classification:

    • E41 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Demand for Money
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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